Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their risk to a reinsurance company. Ruin probabilities allow us to measure the effect of stop-loss reinsurance on the solvency of the primary insurer. They further permit the calculation of the...

Insurance companies need to calculate solvency capital requirements in order to ensure that they can meet their future obligations to policyholders and beneficiaries. The solvency capital requirement is a risk management tool essential for addressing extreme catastrophic events that result in a...

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing...

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call "robustness against optimization". The new notion is studied for...

Motivated by recent advances on elicitability of risk measures and practical considerations of risk optimization, we introduce the notions of Bayes pairs and Bayes risk measures. Bayes risk measures are the counterpart of elicitable risk measures, extensively studied in the recent literature....